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Block #2,924,912

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2018, 4:04:07 AM Β· Difficulty 11.3560 Β· 3,883,733 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
6715ee217a2c4f01f20007296d49b95f8b21a8d05a5f1c938464fdb149c03448
View on Chainz β†—

Height

#2,924,912

Difficulty

11.355974

Transactions

11

Size

72.91 KB

Version

2

Bits

0b5b211e

Nonce

1,476,682,666

Timestamp

11/16/2018, 4:04:07 AM

Confirmations

3,883,733

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

969120fa2cb4781d0422ba36ca1eb393d0bab2cf77dfa0afd112faf56cc4ce76
Transactions (11)
Coinbasee95aefe9f8c8b7…122449d604d023
1 in β†’ 1 out8.5400 XPM110 B
AUhjokok…k5m93PZR
b6e2bbce22802f…5cba4a36f5bf37
50 in β†’ 1 out209.0617 XPM7.27 KB
AFxCAW15…R412hR5v
be7b0d1af1e32c…88de4d05ffca12
50 in β†’ 1 out229.9487 XPM7.28 KB
AFxCAW15…R412hR5v
77368cafa77d3d…99789cd45db34f
50 in β†’ 1 out220.5870 XPM7.27 KB
AFxCAW15…R412hR5v
8d8fa1e38d59e2…d12426085850a1
50 in β†’ 1 out222.5832 XPM7.26 KB
AFxCAW15…R412hR5v
ea6524b314c4d0…ef1d448142efc8
50 in β†’ 1 out234.7684 XPM7.26 KB
AFxCAW15…R412hR5v
5ba2fee220c4c9…5e39db339d366d
50 in β†’ 1 out219.6971 XPM7.27 KB
AFxCAW15…R412hR5v
05f44aa3a18245…944fdc2bea6683
50 in β†’ 1 out244.0743 XPM7.27 KB
AFxCAW15…R412hR5v
e27dc33e718ac4…0f3fe3bc16e54c
50 in β†’ 1 out223.0670 XPM7.27 KB
AFxCAW15…R412hR5v
65c9afad12dc39…b8dd9d61746de5
50 in β†’ 1 out230.1702 XPM7.27 KB
AFxCAW15…R412hR5v
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.054 Γ— 10⁹⁴(95-digit number)
60544496418695049635…71965670594660179039
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
6.054 Γ— 10⁹⁴(95-digit number)
60544496418695049635…71965670594660179039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.054 Γ— 10⁹⁴(95-digit number)
60544496418695049635…71965670594660179041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.210 Γ— 10⁹⁡(96-digit number)
12108899283739009927…43931341189320358079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.210 Γ— 10⁹⁡(96-digit number)
12108899283739009927…43931341189320358081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.421 Γ— 10⁹⁡(96-digit number)
24217798567478019854…87862682378640716159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.421 Γ— 10⁹⁡(96-digit number)
24217798567478019854…87862682378640716161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.843 Γ— 10⁹⁡(96-digit number)
48435597134956039708…75725364757281432319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.843 Γ— 10⁹⁡(96-digit number)
48435597134956039708…75725364757281432321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.687 Γ— 10⁹⁡(96-digit number)
96871194269912079416…51450729514562864639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.687 Γ— 10⁹⁡(96-digit number)
96871194269912079416…51450729514562864641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.937 Γ— 10⁹⁢(97-digit number)
19374238853982415883…02901459029125729279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,713,212 XPMΒ·at block #6,808,644 Β· updates every 60s
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